Smart antenna with no phase calibration for CDMA reverse link

ABSTRACT

The present invention describes an inexpensive as well as efficient smart antenna processor for a code division multiple access (CDMA) wireless communications system, such as a 3 rd  generation (3G) CDMA2000 or W-CDMA system. Separate channel estimation is not required in the present invention, in contrast to a CDMA system with a conventional smart antenna. In addition, the phase distortions due to the different radio frequency (RF) mixers can be automatically compensated in the present invention. Thus, separate phase calibration is not necessary for a smart antenna processor according to the present invention, if the reverse link demodulation is concerned. Furthermore, bit error rate (BER) performance of a CDMA system with the adaptive algorithm in the present invention can be smaller than that of a conventional algorithm, for fading and additive white Gaussian noise (AWGN) environments.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to wireless telecommunications. Moreparticularly, the present invention relates to a design of aninexpensive and efficient smart antenna processor for a code divisionmultiple access wireless communications system. In general, aconventional smart antenna requires phase calibration due to differentcharacteristics at the radio frequency (RF) mixers at a receiver frontend. Phase calibration is an expensive component since it is built Withanalog device in general. The present invention describes a smartantenna processor, which does not require phase calibration.

2. Description of the Related Art

A smart antenna is a blind adaptive antenna array intended to usespatial diversity properties by placing multiple antenna elements in alinear array or other shape. It can enhance the desired signal receptionby suppressing the interference signal with a direction of arrival angle(DOA) different from that of the desired signal. The general techniquesemployed in smart antennas have been developed from adaptive filtertheory.

A smart antenna algorithm discussed in S. Tanaka, M. Sawahashi, and F.Adachi, “Pilot Symbol-Assisted Decision-Directed Coherent Adaptive ArrayDiversity for DS-CDMA Mobile Radio Reverse Link,” IEICE Trans.Fundamentals, Vol. E80-A, pp. 2445-2454, December 1997, “Tanaka I”); S.Tanaka, A. Harada, M. Sawahashi, and F. Adachi, “Transmit DiversityBased on Adaptive Antenna Array for W-CDMA Forward Link,” The 4^(th)CDMA International Conference and Exhibition Proceedings, pp. 282-286,1999, “Tanaka II”); and F. Adachi, M. Sawahashi, and H. Suda, “WidebandDS-CDMA for Next-Generation Mobile Communications Systems,” IEEECommunications Magazine, Vol. 36, No. 9, pp. 56-69, September 1998,“Adachi”) was tested in a field experiment for a 3^(rd) generation (3G)wideband (W)-CDMA wireless communications system. Known pilot symbolpatterns are inserted into a common control channel in a W-CDMA system,as discussed for example in 3rd Generation Partnership Project,“Physical Channels and Mapping of Transport Channels onto PhysicalChannels (FDD),” 3GPP Technical Specification, TS25.211, v3.2.0, March,2000; 3rd Generation Partnership Project, “Spreading and Modulation(FDD),” 3GPP Technical Specification, TS25.213, v3.2.0, March., 2000;and 3rd Generation Partnership Project, “FDD: Physical LayerProcedures,” 3Gpp Technical Specification, TS25.214, v3.2.0, March, 2000(collectively “3GPP”). On the other hand, a pilot channel is used in a3G CDMA2000 system, such as discussed in TIA, Interim V&V Text forcdma2000 Physical Layer (Revision 8.3), Mar. 16, 1999 “TIA”). A smartantenna processor generates a weight vector w(k) at the k-th snapshot(i.e., iteration). The smart antenna algorithms such as those proposedby Tanaka I, Tanaka II and Adachi try to let the weight vector convergeto the array response vector a(θ)=[1, e^(−jπ sin θ), . . . ,e^(−j(M−1)π sin θ)] rather than the total input phase vector includingthe fading phase, different mixer phase distortion and array phasedifference, where θ is the DOA from the desired signal, M is the numberof antenna array elements, e is the exponential operator, and π is3.14159. Also, the updated weight vector in Tanaka I, Tanaka II andAdachi is used in a channel estimation block to estimate and cancel thefading phase. Furthermore, the phase and amplitude of each array elementin the smart antenna-parallel radio frequency (RF) base station receivercircuitry are different from those of other receiver unit, and vary asthe received signal power changes, see Tanaka II. Fortunately, themeasured data indicate that phase difference between RF receiver unitsis almost constant, and amplitude difference is almost zero even thereceived signal power changes. Therefore, phase calibration wassuggested before the adaptation processing, in Tanaka II. Phasecalibration is an expensive component.

The least mean square (LMS) adaptive algorithm, which is an art relatedto the present invention, has been known for its simplicity because theLMS does not require any calculations of correlation functions or matrixinversion. For example, the weight vector in Simon Haykin, “AdaptiveFilter Theory,” pp. 437, Summary of The NLMS Algorithm, Prentice Hall,1996 (“Haykin”) was updated for a general adaptive filter application byusing the normalized least mean square (N-LMS) algorithm. And, it hasbeen shown that the N-LMS algorithm in Haykin not only shows a fasterconvergence than the LMS algorithm but also overcomes the gradient noiseamplification problem existing in the LMS algorithm. The N-LMS algorithmlets the output converge to the desired adaptation processing output.The N-LMS algorithm minimizes the mean square estimation error betweenthe desired output and the adaptation processing output.

BRIEF SUMMARY OF THE INVENTION

It is an object of the present invention to provide an inexpensive andefficient smart antenna processor useful in a wireless communicationssystem, such as a code division multiple access (CDMA) wirelesscommunications system, e.g., a 3^(rd) generation (3G) CDMA2000 or W-CDMAsystem. Separate channel estimation is not required in the presentinvention. In addition, the phase distortion due to the radio frequency(RF) mixer in each antenna element can be compensated automatically bythe present invention. Thus, the phase calibration is not necessary fora smart antenna processor in the present invention if the reverse linkdemodulation is concerned. One embodiment of the present invention isobtained by modifying the normalized least mean square (MN-LMS) adaptivefilter. This requires only (5M+2) complex multiplication and (4M+1)complex additions per snapshot. Finally, bit error rate (BER)performance of a CDMA system with the MN-LMS algorithm in the presentinvention is better than that with the conventional N-LMS algorithm.

The present invention is a modified and normalized (MN)-LMS adaptivefilter, which can track the individual total input phase at eachelement. The individual total input phase consists of the DOA, fadingphase, and the phase distortion due to the mixer. The smart antenna inthe presentation can track the individual total input phase at eachelement. In addition, the smart antenna algorithm in the presentinvention can be applied for both W-CDMA and CDMA2000 systems while thesmart antenna in Tanaka I, Tanaka II and Adachi was tested for only aW-CDMA system. Furthermore, the present invention presents aninexpensive smart antenna because the W-CDMA or CDMA2000 system with theMN-LMS algorithm in the present invention does not require either anyphase calibration or any channel estimation for data demodulationpurpose.

In accordance with one aspect of the invention, there is provided amethod and system for receiving a signal for use in combination withwireless communications. A signal is received in a plurality ofantennas. The received signal is processed utilizing an updated weightvector, wherein the updated weight vector compensates substantially fora phase distortion of the signal.

According to one alternative aspect of the invention, the receivedsignal is processed according to an MN-LMS algorithm. According to amore specific alternative aspect of the invention, the received signalis processed according to $\begin{matrix}{{{\underset{\_}{w}}_{l}\left( {i + 1} \right)} = \quad {{{\underset{\_}{w}}_{l}(i)} + {\frac{\mu}{a + {{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}}^{2}} \times \left\lbrack {{M{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}} - {{{\underset{\_}{\overset{\sim}{y}}}_{l}^{H}(i)}{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}{{\underset{\_}{w}}_{l}(i)}}} \right\rbrack}}} \\{= \quad {{{\underset{\_}{w}}_{l}(i)} + {\frac{\mu}{a + {{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}}^{2}} \times {\left\lbrack {{M{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}} - {{{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}}^{2}{{\underset{\_}{w}}_{l}(i)}}} \right\rbrack.}}}}\end{matrix}$

According to another alternative aspect of the invention, the receivedsignal is processed according to an N-LMS algorithm. According to a morespecific alternative aspect of the invention, the received signal isprocessed according to${{\underset{\_}{w}}_{l}\left( {i + 1} \right)} = {{{\underset{\_}{w}}_{l}(i)} + {\frac{\mu}{a + {{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}}^{2}} \times {\left\lbrack {{M{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}} - {{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}{{\underset{\_}{\overset{\sim}{y}}}_{l}^{H}(i)}{{\underset{\_}{w}}_{l}(i)}}} \right\rbrack.}}}$

The antennas may be a multiple antenna array, or may be multipleantennas. In accordance with further aspects of the invention, theantennas may be in a base station, or a mobile station.

According to another aspect of the invention, the method and system donot include phase calibration.

BRIEF DESCRIPTION OF THE DRAWINGS

The features, objects, and advantages of the present invention willbecome more apparent from the detailed description set forth below whentaken in conjunction with the drawings in which like referencecharacters identify correspondingly throughout and wherein:

FIG. 1 shows a base station receiver block diagram with a smart antennafor a W-CDMA reverse link in accordance with one embodiment of thepresent invention;

FIG. 2 shows a base station receiver block diagram with a smart antennafor a CDMA2000 reverse link in accordance with one embodiment of thepresent invention;

FIGS. 3A-3C show angle tracking capability of a smart antenna with theN-LMS for W-CDMA in accordance with one embodiment of the presentinvention;

FIGS. 4A-4C show angle tracking capability of a smart antenna with theMN-LMS for W-CDMA in accordance with one embodiment of the presentinvention;

FIG. 5 shows simulation BER results for a W-CDMA system with smartantennas by using the MN-LMS and N-LMS algorithms, where M is the numberof array antenna elements, in accordance with one embodiment of thepresent invention; and

FIG. 6 shows simulation BER results for a CDMA2000 system with smartantennas by using the MN-LMS and N-LMS algorithms, where M is the numberof array antenna elements, in accordance with one embodiment of thepresent invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention can be applied to a general CDMA system as long aseither a pilot channel or a pilot symbol assisted channel is used. The3G W-CDMA system employs a pilot symbol assisted channel such asdiscussed in 3GPP while the CDMA2000 system a pilot channel, such as inTIA. Thus, the present invention can be applied to both W-CDMA andCDMA2000 systems. A W-CDMA system and a smart antenna with the N-LMSalgorithm are reviewed. Then, a smart antenna with the MN-LMS algorithmis described later.

W-CDMA SYSTEM MODEL

Spreading is applied to conventional uplink physical channels for aW-CDMA system. It consists of two operations. The first is achannelization operation, which transforms every data symbol into anumber of chips, thus increasing the bandwidth of the signal. The numberof chips per data symbol is called the Spreading Factor (SF). The secondoperation is the scrambling operation, where a scrambling code isapplied to the spread signal. One example of spreading is discussed in3GPP on “Spreading and Modulation”, p. 7.

With the channelization, data symbol, so-called I- and Q-branches areindependently multiplied with an orthogonal variable spreading factor(OVSF) code. With the scrambling operation, the resultant signals on theI- and Q-branches are further multiplied by complex-valued scramblingcode, where I and Q denote real and imaginary parts, respectively (see3GPP, “Spreading and Modulation”, p. 7). One dedicated physical controlchannel (DPCCH) and up to six parallel dedicated physical data channels(DPDCHs) can be transmitted simultaneously, i.e., 1≦n≦6. The binaryDPCCH and DPDCHs to be spread are represented by real-valued sequences,i.e., the binary value “0” is mapped to the real value +1, while thebinary value “1” is mapped to the real value −1. The DPCCH is spread tothe chip rate by the channelization code C_(ch,0), while the n-th DPDCHcalled DPDCH_(n) is spread to the chip rate by the channelization codeC_(ch,n). The channelization codes are uniquely described asC_(Ch,SF,k), where SF is the spreading factor of the code and k is thecode number, 0≦k≦SF−1. A definition of the generation method for thechannelization code can be found in 3GPP on “Spreading and Modulation”,p. 11. In the present invention, only one DPDCH is taken fordemonstration purposes, and the DPCCH and DPDCH are spread byC_(ch,256,0)=(1, 1, . . . , 1) and C_(ch,4,k=2)=(1,−1,1,−1),respectively.

The signal formats and notations for the system model are written as

a base band DPDCH signal=C _(ch,4,k=2)(i)d _(DPDCH)(i)  (1)

a base band DPCCH signal=C _(ch,256,0)(i)d _(DPCCH)(i)  (2)

long and/or short scrambling codes used by transmitter=a ^(I)(i)+ja^(Q)(i)  (3)

a base band transmitted signal=[C _(ch,4,k=2)(i)d _(DPDCH)(i)+jC_(ch,256,0)(i)d _(DPCCH)(i)](a ^(I)(i)+ja ^(Q)(i))  (4)

a base band received signal at a reference element in a smart antennaunder fading and AWGN environment=[C _(ch,4,k=2)(i)d _(DPDCH)(i)+jC_(ch,256,0)(i)d _(DPCCH)(i)](a ^(I)(i)+ja ^(Q)(i))α(i)e ^(jφ(i)) +n₀(i)  (5)

and a base band de-scrambled signal at a receiver=[C _(ch,4,k=2)(i)d_(DPDCH)(i)+jC _(ch,256,0)(i)d _(DPCCH)(i)]α(i)e^(jφ(i)) +n(i)  (6)

where

i is the chip index,

j={square root over (−1)},

e is the exponential operator,

d_(DPDCH)(i)=±1 valued DPDCH data at the i-th chip,

d_(DPCCH)(i)=±1 valued DPCCH pilot symbol data at the i-th chip,

a^(I)(i)=±1 valued real part of a complex pseudonoise (PN) spreadingsequence,

a^(Q)(i)=±1 valued imaginary part of a complex PN spreading sequence,

α(i) is the amplitude of a fading multipath,

φ(i) is the phase of a fading multipath,

n₀(i) is the additive white Gaussian noise (AWGN) representing both thethermal noise and multiple access interference from other users, and

n(i) is the PN despread AWGN at the i-th chip.

A DPCCH frame takes 10 ms, and consists of 15 slots. Each slot takes0.67 ms, and consists of 10 control information bits (or symbols), whichare composed of pilot bits, transmit power-control (TPC) command bits,feedback information (FBI) bits, and an optional transport-formatcombination indicator bit (TFCI). The spreading factor for each symbolin the DPCCH is 256. Accordingly, the total number of chips in one slotis 2,560.

FIG. 1 shows a base station block diagram with smart antenna 101 a-101Mfor a W-CDMA reverse link. Thermal noise 103 is added to the signals,and mixers 105 introduce different phase distortions. A matched filter107 is performed on each signal, and sampled every chip T_(c) and then aPN despread 109 is performed. Using the orthogonal property betweendifferent channel spreading codes, the average of equation (6) over Nchip intervals (where N=256 is the number of chips per pilot symbolinterval) can be approximated as $\begin{matrix}{{{\frac{1}{N}{\sum\limits_{i = 1}^{N}{\left\lbrack {{{C_{{ch},4,{k = 2}}(i)}{d_{DPDCH}(i)}} + {{{jC}_{{ch},256.0}(i)}{d_{DPCCH}(i)}}} \right\rbrack {\alpha (i)}^{j\quad {\varphi {(i)}}}}}} + {\eta (i)}} \approx {j\quad d_{DPCCH}\alpha^{j\quad \varphi}}} & (7)\end{matrix}$

since the average of PN despread noise components is zero, and amplitudeα(i) and phase φ(i) of a multipath are almost constant during a pilotsymbol interval when the mobile velocity is less than 100 km/h. “Avg.256 chips” 113 performs this average function for each element.

The de-scrambled signals in equation (6) are written in an M×1 vectorfor a smart antenna with M array elements as $\begin{matrix}{{{\underset{\_}{x}}_{l}(i)} = {\begin{bmatrix}{x_{l,1}(i)} \\\vdots \\{x_{l,M}(i)}\end{bmatrix} = {{\left\lbrack {{{C_{{ch},4,k}(i)}{d_{DPDCH}(i)}} + {j\quad {d_{DPCCH}(i)}}} \right\rbrack {\alpha_{l}(i)}{^{j\quad {\varphi_{l}{(i)}}}\begin{bmatrix}^{j\quad \phi_{1}} \\^{{- j}\quad {({{\pi \quad \sin \quad {\theta {(i)}}} - \phi_{2}})}} \\\vdots \\^{{- j}\quad {({{{({M - 1})}\quad \sin \quad {\theta {(i)}}} - \phi_{M}})}}\end{bmatrix}}} + {\underset{\_}{n}(i)}}}} & (8)\end{matrix}$

where C_(ch,256,0)(i) is I for all i and dropped in equation (8), i runsfrom 1 to 2560 for the first slot interval, φ_(m) is the phasedistortion at the m-th mixer, m=1, 2, . . . , M, θ(i) is the DOA fromthe desired user at the i-th chip, the first element in the antennaarray is used as a reference, the antenna spacing is a half wave length,and l means the multipath index called finger index, l=1, 2, . . . , L.The multipath delays are omitted without loss of generality in equation(8) since the finger outputs with the different multipath delays arealigned and combined at a Rake receiver discussed later. Equation (8)describes the output of the PN despreading. The block named by “PNDespread” 109 performs the PN despreading function.

Pilot symbol patterns are known to a base station receiver for channelestimation purpose. The smart antenna in the present invention isactivated for the pilot symbol intervals. The number of pilot symbolsper slot, N_(pilot), can be 3, 4, 5, 6, 7, and 8 for example. Forexample, when N_(pilot), is equal to 8, the smart antenna is applied forthe first 8×256 chips every slot. The data in the last 2×256 chips arenot used for the channel estimation purpose. Therefore, the data to beemployed by a smart antenna would be x_(l)(i), i=1, 2, . . . , 8×256every slot. “Chop data” 111 performs this function.

Multiplying the known pilot symbol pattern d_(DPCCH)(i) to equation (8),the signal can be written as $\begin{matrix}{{{\underset{\_}{y}}_{l}(i)} = {\begin{bmatrix}{y_{l,1}(i)} \\\vdots \\{y_{l,M}(i)}\end{bmatrix} = {{{d_{DPCCH}(i)}{{\underset{\_}{x}}_{l}(i)}} = {{\left\lbrack {{{C_{{ch},4,k}(i)}{d_{DPDCH}(i)}\quad {d_{DPCCH}(i)}} + j} \right\rbrack {\alpha_{l}(i)}{^{j\quad {\varphi_{l}{(i)}}}\begin{bmatrix}^{j\quad \phi_{1}} \\^{{- j}\quad {({{\pi \quad \sin \quad {\theta {(i)}}} - \phi_{2}})}} \\\vdots \\^{{- j}\quad {({{{({M - 1})}\quad \sin \quad {\theta {(i)}}} - \phi_{M}})}}\end{bmatrix}}} + {{\underset{\_}{n}(i)}.}}}}} & (9)\end{matrix}$

“Pilot symbol pattern” 119 generates the corresponding pilot symbolpattern. The signal component with data d_(DPDCH)(i) in equation (9) canbe completely suppressed by averaging y_(l)(i) over N=256 chips. “Avg.256 chips” 113 performs this averaging function as explained forequation (6). The M×1 average output vector is denoted by {tilde over(y)} _(l)(k_(obs)) for finger l, and written as $\begin{matrix}{{{\underset{\_}{\overset{\sim}{y}}}_{l}\left( k_{obs} \right)} = {\begin{bmatrix}{{\overset{\sim}{y}}_{l,1}\left( k_{obs} \right)} \\\vdots \\{{\overset{\sim}{y}}_{l,1}\left( k_{obs} \right)}\end{bmatrix} = {\frac{\sum\limits_{i = {{{({k_{obs} - 1})}N} + 1}}^{k_{obs}N}{{\underset{\_}{y}}_{l}(i)}}{N} = {{j\quad {\alpha_{l}\left( {k_{obs}N} \right)}{^{j\quad {\varphi_{1}{({k_{obs}N})}}}\begin{bmatrix}^{j\quad \phi_{1}} \\^{{- j}\quad {({{\pi \quad \sin \quad {\theta {({k_{obs}N})}}} - \phi_{2}})}} \\\vdots \\^{{- j}\quad {({{{({M - 1})}\quad \sin \quad {\theta {({k_{obs}N})}}} - \phi_{M}})}}\end{bmatrix}}} + {\underset{\_}{\overset{\sim}{n}}\left( k_{obs} \right)}}}}} & (10)\end{matrix}$

where k_(obs) denotes the observation index with observation intervalNT_(c), the OVSF modulated traffic channel data d_(DPDCH)(i) issuppressed after N chip averaging, i.e.,${\sum\limits_{i = {{{({k_{obs} - 1})}N} + 1}}^{k_{obs}N}{{C_{{ch},4,k}(i)}{d_{DPDCH}(i)}\quad {d_{DPCCH}(i)}}} = 0$

due to the orthogonality, and ñ(k_(obs)) is the averaged noisecomponent. The change of DOA during an observation interval NT_(c) wouldbe θ(k_(obs)N)−θ((k_(obs)−1)N)=νNT_(c)/R where R is the distance fromthe base station to a mobile and ν is the mobile velocity. The DOA θ(i)in equation (9) is almost constant during an observation interval when amobile velocity is less than 300 km/h.

The {tilde over (y)} _(l)(k_(obs)) is repeated N times for the smartantenna processing if the update rate for the smart antenna weightvector is equal to the chip rate. The number of repetition decreasesproportionally as the snapshot (i.e., update rate) decreases. Therepeated sequence, which is the input to the smart antenna, is writtenas

{tilde over (y)} _(l)(i)={tilde over (y)} _(l)(k _(obs) N) for (k _(obs)−1) N≦i≦k _(obs) N.  (11)

“Repeat N=256” 115 performs the repetition. The output of the “RepeatN=256” block 115 is input to the smart antenna processor 117. Two smartantenna processors are compared below. One is a smart antenna with aconventionally known adaptive algorithm named N-LMS (Haykin, p. 437) andthe other one is with the novel adaptive algorithm described in thepresent invention named MN-LMS. First, N-LMS is reviewed and then MN-LMSis described later.

N-LMS ALGORITHM

Suppose that the snapshot rate is equal to the chip rate. The input tothe smart antenna in FIG. 1 can be written as $\begin{matrix}{{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)} = {\begin{bmatrix}{{\overset{\sim}{y}}_{l,1}(i)} \\\vdots \\{{\overset{\sim}{y}}_{l,M}(i)}\end{bmatrix} = {{j\quad {\alpha_{l}(i)}{^{j\quad {\varphi_{l}{(i)}}}\begin{bmatrix}^{j\quad \phi_{1}} \\^{{- j}\quad {({{\pi \quad \sin \quad {\theta {(i)}}} - \phi_{2}})}} \\\vdots \\^{{- j}\quad {({{{({M - 1})}\quad \sin \quad {\theta {(i)}}} - \phi_{M}})}}\end{bmatrix}}} + {\underset{\_}{\overset{\sim}{n}}(i)}}}} & (12)\end{matrix}$

for the i-th chip time. According to the N-LMS algorithm in Haykin, p.437, the updated weight vector w _(l)(i+1) for finger l and snapshot ican be written as $\begin{matrix}{{{\underset{\_}{w}}_{l}\left( {i + 1} \right)} = {{{\underset{\_}{w}}_{l}(i)} + {\frac{\mu}{a + {{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}}^{2}}\left\lbrack {{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}{e_{l}^{*}(i)}} \right\rbrack}}} & (13)\end{matrix}$

where

e _(l)*(i)=M−{tilde over (y)} _(l) ^(H)(i)w _(l)(i)  (14)

H denotes the Hermitian operation, i.e., conjugate and transpose, *denotes the conjugate operation, ∥x∥ is the norm of vector x, a is apositive constant, μ is a constant convergence parameter, 0<μ<2, and w^(H)(i)w(i) becomes M when the weight vector w(i) perfectly matches withthe vector [e^(jφ), e^(−j(π sin θ(i)−φ) ^(₂) ⁾, . . . ,e^(−j((M−1)π sin θ(i)−φ) ^(_(M)) ⁾]^(T), which is similar to the arrayresponse vector. Therefore, M is used as a reference in equation (14)for the conventional N-LMS algorithm. The weight vector w _(l)(i) is theoutput for the conventional N-LMS algorithm at the “MN-LMS or N-LMSSmart Antenna” 117 in FIG. 1.

The weight vector in equation (13) is updated by measuring theestimation error described in equation (14), i.e., the differencebetween the desired reference M and the smart antenna output {tilde over(y)} _(l) ^(H)(i)w _(l)(i). When the smart antenna generates an idealweight vector, {tilde over (y)} _(l) ^(H)(i)w _(l)(i) is equal to M witha proper normalization, and error in equation (14) will be zero.

MODIFIED N-LMS ALGORITHM

By substituting equation (14) into equation (13), the principle of thepresent invention can be explained. In other words, $\begin{matrix}{{{\underset{\_}{w}}_{l}\left( {i + 1} \right)} = {{{\underset{\_}{w}}_{l}(i)} + {\frac{\mu}{a + {{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}}^{2}} \times {\left\lbrack {{M{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}} - {{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}{{\underset{\_}{\overset{\sim}{y}}}_{l}^{H}(i)}{{\underset{\_}{w}}_{l}(i)}}} \right\rbrack.}}}} & (15)\end{matrix}$

The N-LMS algorithm was derived by replacing the autocorrelation matrixR_({tilde over (y)}) _(l) _({tilde over (y)}) _(l) (i) with aninstantaneous estimate {tilde over (y)} _(l)(i){tilde over (y)} _(l)^(H)(i) in equation (15). For the present invention, the M×Minstantaneous correlation matrix {tilde over (y)} _(l)(i){tilde over(y)} _(l) ^(H)(i) in equation (15) is further replaced with a scalar{tilde over (y)} _(l) ^(H)(i){tilde over (y)} _(l)(i). Then, the updatedweight vector w _(l)(i+1) of the MN-LMS algorithm is written as$\begin{matrix}\begin{matrix}{{{\underset{\_}{w}}_{l}\left( {i + 1} \right)} = \quad {{{\underset{\_}{w}}_{l}(i)} + {\frac{\mu}{a + {{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}}^{2}} \times \left\lbrack {{M{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}} - {{{\underset{\_}{\overset{\sim}{y}}}_{l}^{H}(i)}{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}{{\underset{\_}{w}}_{l}(i)}}} \right\rbrack}}} \\{= \quad {{{\underset{\_}{w}}_{l}(i)} + {\frac{\mu}{a + {{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}}^{2}} \times \left\lbrack {{M{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}} - {{{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}}^{2}{{\underset{\_}{w}}_{l}(i)}}} \right\rbrack}}}\end{matrix} & (16)\end{matrix}$

where a is a positive constant and μ is the convergence parameter,0<μ<2.

Suppose that the updated weight vector w _(l)(i) approaches the receivedvector {tilde over (y)} _(l)(i). Then ∥{tilde over (y)} _(l)(i)∥² inequation (16) is close to M under AWGN environment from equation (12)and the bracket in equation (16) becomes zero vector. The weight vectorwill be in steady state. This is a rationale for replacing term {tildeover (y)} _(l)(i){tilde over (y)} _(l) ^(H)(i) in equation (15) with ascalar {tilde over (y)} _(l) ^(H)(i){tilde over (y)} _(l)(i) for thepresent invention. In addition, solution of the weight vector satisfyingequation (16) will be unique and will be the received vector {tilde over(y)} _(l)(i). Therefore, the input phase of the received signal at eachantenna element can be tracked. However, the solution of the weightvector for the N-LMS algorithm in equation (15) does not need to beunique. As long as the inner product {tilde over (y)} _(l) ^(H)(i)w_(l)(i) in equation (14) approaches M, error e_(l)(i) will approach zeroand many such weight vectors can minimize the mean square error inequation (14). This is why the matrix {tilde over (y)} _(l)(i){tildeover (y)} _(l) ^(H)(i) is replaced with {tilde over (y)} _(l)^(H)(i){tilde over (y)} _(l)(i) in equation (16).

The inner product {tilde over (y)} _(l) ^(H)(i){tilde over (y)}_(l)(i)=∥{tilde over (y)} _(l)(i)² is approximately equal to Mα²(i)under fading environment by using equation (12). It is desirable for thebracket term in equation (16) to be zero. Therefore, the weight vectorwould converge to w _(l)(i)={tilde over (y)} _(l)(i)/α_(l) ²(i) and$\begin{matrix}{{{\underset{\_}{w}}_{l}(i)} = {{\frac{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}{\alpha_{l}^{2}(i)} \approx {\frac{j\quad {\alpha_{1}(i)}^{j\quad {\varphi_{l}{(i)}}}}{\alpha_{l}^{2}(i)}\begin{bmatrix}^{j\quad \phi_{1}} \\^{{- j}\quad {({{\pi \quad \sin \quad {\theta {(i)}}} - \phi_{2}})}} \\\vdots \\^{{- j}\quad {({{{({M - 1})}\quad \sin \quad {\theta {(i)}}} - \phi_{M}})}}\end{bmatrix}}} = {\frac{1}{\alpha_{l}(i)}j\quad {^{j\quad {\varphi_{l}{(i)}}}\begin{bmatrix}^{j\quad \phi_{1}} \\^{{- j}\quad {({{\pi \quad \sin \quad {\theta {(i)}}} - \phi_{2}})}} \\\vdots \\^{{- j}\quad {({{{({M - 1})}\quad \sin \quad {\theta {(i)}}} - \phi_{M}})}}\end{bmatrix}}}}} & (17)\end{matrix}$

in an ideal case. The weight vector in equation (17) is the output ofthe MN-LMS smart antenna and shown at the output of “MN-LMS or N-LMSSmart Antenna” 117 in FIG. 1. The weight vector is normalized at 121 andwritten as $\begin{matrix}{{{\underset{\_}{\overset{\sim}{w}}}_{l}(i)} = {\begin{bmatrix}{{\overset{\sim}{w}}_{l,1}(i)} \\\vdots \\{{\overset{\sim}{w}}_{l,M}(i)}\end{bmatrix} = {\frac{{\underset{\_}{w}}_{l}(i)}{{{\underset{\_}{w}}_{l}^{H}(i)}{{{\underset{\_}{w}}_{l}(i)}/M}} = {j\quad {\alpha_{l}(i)}{{^{i\quad {\varphi_{l}{(i)}}}\begin{bmatrix}^{j\quad \phi_{1}} \\^{{- j}\quad {({{\pi \quad \sin \quad {\theta {(i)}}} - \phi_{2}})}} \\\vdots \\^{{- j}\quad {({{{({M - 1})}\quad \sin \quad {\theta {(i)}}} - \phi_{M}})}}\end{bmatrix}}.}}}}} & (18)\end{matrix}$

The normalized weight vector in equation (18) is shown at the output of“Normalization” 121 in FIG. 1.

The normalized weight vector 121 is averaged every slot interval at “Avg256×8 chips” 123, and repeated at “Repeat 256×10 times” 125 in FIG. 1.The output of “Repeat 256×10 times” 125 in FIG. 1 is written as$\begin{matrix}{{{{\underset{\_}{\overset{\_}{w}}}_{l}(i)} = {{\frac{1}{\left( {N_{pilot} = 8} \right) \times 256}{\sum\limits_{i^{\prime} = 1}^{{({N_{p} = 8})} \times 256}{{{\underset{\_}{\overset{\sim}{w}}}_{l}\left( i^{\prime} \right)}\quad {for}\quad i}}} = 1}},\ldots \quad,2560.} & (19)\end{matrix}$

{overscore (w)} _(l)(i) is a new weight vector which compensatesautomatically for phase distortion. Note that no separate phasecalibration was required, since the new weight vector automaticallycompensates. The demodulation output z_(l)(i) with a smart antenna arrayis obtained by taking the inner-product between the averaged normalizedweight vector {overscore (w)} _(l)(i) and the received signal vector x_(l)(i) in equation (8) at $\sum\limits_{M}$

127 in FIG. 1. The output z_(l)(i) is written as

z _(l)(i)={overscore (w)} _(l) ^(H)(i)x _(l)(i)≈Mα_(l) ²(i)[d_(DPCCH)(i)−jC _(ch,4,k)(i)d _(DPDCH)(i)]  (20)

where l=1, . . . , L and i=1, 2, . . . , 2560. The demodulation outputz_(l)(i) at each finger l,1=1, . . . , L, are combined 129 andmultiplied with the OVSF code C_(ch,4k)(i) for a Rake receiver, and thenaccumulated. The decision variable R_(DPDCH) for the k_(bit)-th isoutput 131, and can be approximately written as

R _(DPDCH)(k _(bit))≈−jcd _(DPDCH)(k _(bit))  (21)

where c is a positive constant and k_(bit) is the traffic channel bitindex. The final soft decision value can be obtained asR_(DPDCH)(k_(bit))/(−j) for a soft decision decoder. The hard decisionvalue would be the sign of R_(DPDCH)(k_(bit))/(−j) and can be used for ahard decision decoder.

CDMA2000 SYSTEM MODEL

A mobile station in a CDMA2000 reverse link transmits a pilot and atraffic data channel together, which are orthogonal to each otherthrough Walsh modulation. The pilot channel in a CDMA2000 system isalways “on” while the pilot symbol inserted channel in a W-CDMA systemis “on” during only pilot symbol intervals. Although a mobile stationmay transmit several traffic data channels simultaneously, only onetraffic channel is assumed for simplicity and demonstration of thepresent invention. Most materials in this section are parallel to thoseused for W-CDMA in sections 1, 2, and 3 above. The transmitted band passsignal s_(r)(t) in the reverse link can be written as

s _(r)(t)=Re[u _(r)(t)e ^(j2πfct)]  (22)

where u_(r)(t) is a base band complex envelope. The base band complexsignal u_(r)(t) can be written as

u _(r)(t)=[A(t)+jB(t)][a ^(I)(t)+ja ^(Q)(t)]  (23)

where

A(t) represents the pilot channel signal which is a constant,

B(t)=d_(trafic)(t) W₂ ⁴(t) is a Walsh modulated traffic channel,

d_(trafic)(t) is a traffic data channel of ±1,

W₂ ⁴(t) is a Walsh symbol of (+1−1+1−1) four chips and,

a^(I)(t) and a^(Q)(t) are I and Q short PN sequences, respectively.

FIG. 2 shows a block diagram for a base station receiver for a CDMA2000reverse link with either the MN-LMS in the present invention or aconventional N-LMS smart antenna algorithm. A linear antenna array of Melements is used, and the antenna array response vector a(θ) is writtenas a(θ)=[1e^(−jπ sin θ) . . . e^(−j(M−)π sin θ)]^(T) where θ is the DOAfrom the desired signal and the antenna spacing is a half wave length.

The received signal from antennas 101 a-101M is frequency down-convertedand thermal noise 103 is added in FIG. 2. The RF mixers 105 introducedifferent phase distortions, φ₁, φ₂, . . . , φ_(M), as those in FIG. 1.The down converted signals are fed into the matched filters “MF” 107 inFIG. 2, and then sampled every chip T_(c). The samples from M antennaelements are formed into a vector. The sampled M×1 vector at iT_(c) isPN despread with a complex PN sequence (a^(I)(i)+ja^(Q)(i)) at “PNDespread” 109 in FIG. 2, and written as $\begin{matrix}{{{\underset{\_}{y}}_{l}(i)} = {\left\lbrack \quad \begin{matrix}{y_{l,1}(i)} \\\vdots \\{y_{l,M}(i)}\end{matrix} \right\rbrack = {{\left\lbrack {{A(i)} + {j\quad {B(i)}}} \right\rbrack {\alpha_{l}(i)}{^{j\quad {\varphi_{l}{(i)}}}\begin{bmatrix}^{j\quad \phi_{1}} \\^{{- j}\quad {({{\pi \quad \sin \quad {\theta {(i)}}} - \phi_{2}})}} \\\vdots \\^{{- j}\quad {({{{({M - 1})}\quad \sin \quad {\theta {(i)}}} - \phi_{M}})}}\end{bmatrix}}} + {\underset{\_}{\hat{n}}(i)}}}} & (24)\end{matrix}$

where

i denotes the chip index,

l denotes the finger (multipath) index, l=1, . . . , L,

αn_(l)(i) is the amplitude of the l-th multipath,

φ_(l)(i) is the phase of the l-th multipath, and

{circumflex over (n)}(i) represents the noise vector of AWGN plusinterference due to other user signals.

The channel estimation including a_(l)(i), φ_(l)(i), θ_(l)(i), and φ_(m)together in equation (24) can be obtained by accumulating y _(l)(i) overa multiple of Walsh symbols and using the Walsh orthogonal property at“Avg. N_(pilot) chips” 201 in FIG. 2. The output vector {tilde over (y)}_(l)(k) after Avg. N_(pilot) chip accumulation can be written as$\begin{matrix}\begin{matrix}{{{\underset{\_}{\overset{\sim}{y}}}_{l}(k)} = \quad {\left\lbrack \quad \begin{matrix}{{\overset{\sim}{y}}_{l,1}(k)} \\\vdots \\{{\overset{\sim}{y}}_{l,M}(k)}\end{matrix} \right\rbrack = {\sum\limits_{i = {{{({k - 1})}N_{pilot}} + 1}}^{{kN}_{pilot}}{{\underset{\_}{y}}_{l}(i)}}}} \\{= \quad {N_{pilot}{A\left( {kN}_{pilot} \right)}{\alpha_{l}\left( {kN}_{pilot} \right)}^{j\quad {\varphi_{l}{({kN}_{pilot})}}}}} \\{\quad {\begin{bmatrix}^{j\quad \phi_{1}} \\^{{- j}\quad {({{\pi \quad \sin \quad {\theta {({kN}_{pilot})}}} - \phi_{2}})}} \\\vdots \\^{{- j}\quad {({{{({M - 1})}\quad \sin \quad {\theta {({kN}_{pilot})}}} - \phi_{M}})}}\end{bmatrix} + {\underset{\_}{\overset{\sim}{n}}\left( {kN}_{pilot} \right)}}}\end{matrix} & (25)\end{matrix}$

where k denotes a channel observation index with observation intervalequal to N_(pilot)T_(c), and Walsh modulated traffic channel datadisappears after N_(pilot) chip accumulation, i.e.,${\sum\limits_{i = {{{({k - 1})}N_{pilot}} + 1}}^{{kN}_{pilot}}\left\{ {{B(i)} = {{W_{2}^{4}(i)}{d_{t}(i)}}} \right\}} = 0$

due to the Walsh orthogonality every bit.

It is reasonable to choose N_(pilot)=256 chips from the results becausethe multipath amplitude, phase, and the DOA are almost constant duringan observation interval. The output vector {tilde over (y)} _(l)(k) isrepeated N_(pilot) times to update the weight vector “Repeat N_(pilot)times” 203 in FIG. 2 if the smart antenna snapshot rate is equal to thechip rate. The number of repetitions decreases as the snap shot ratedecreases. The repeated sequence, which is the input to the smartantenna 117, is written as

{tilde over (y)} _(l)(i){tilde over (y)} _(l)(kN _(pilot)) for (k−1)N_(pilot) ≦i≦kN _(pilot).  (26)

The input to the smart antenna 117 in FIG. 2 for the i-th chip intervalis written as $\begin{matrix}{{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)} = {{N_{pilot}{A(i)}{\alpha_{l}(i)}{^{j\quad {\varphi_{l}{(i)}}}\begin{bmatrix}^{j\quad \phi_{1}} \\^{{- j}\quad {({{\pi \quad \sin \quad {\theta {(i)}}} - \phi_{2}})}} \\\vdots \\^{{- j}\quad {({{{({M - 1})}\quad \sin \quad {\theta {(i)}}} - \phi_{M}})}}\end{bmatrix}}} + {\underset{\_}{\overset{\sim}{n}}(i)}}} & (27)\end{matrix}$

for both the N-LMS in equation (13) and MN-LMS algorithm in equation(16).

The weight vector w _(l)(i) is obtained by using equation (13) and (16)with input {tilde over (y)} _(l)(i) in equation (27) for the N-LMS andMN-LMS algorithms, respectively. The weight vector is normalized at“Normalization” 121 in FIG. 2, and denoted as {tilde over (w)} _(l)(i).The smart antenna output is obtained by taking the inner-product betweenthe normalized weight vector {tilde over (w)} _(l)(i)and the receivedsignal vector y _(l)(i) (not {tilde over (y)} _(l)(i) ). The arrayoutput is denoted as z_(l)(i) at $\sum\limits_{M}$

127 in FIG. 2, and is written as $\begin{matrix}{{z_{l}(i)} = {{{{\underset{\_}{\overset{\sim}{w}}}_{l}^{H}(i)}{{\underset{\_}{y}}_{l}(i)}} = {{\left\lbrack \frac{{\underset{\_}{w}}_{l}(i)}{{{\underset{\_}{w}}_{l}^{H}(i)}{{{\underset{\_}{w}}_{l}(i)}/M}} \right\rbrack^{H}{{\underset{\_}{y}}_{l}(i)}} \approx {{{MA}(i)}\left( {{A(i)} + {j\quad {B(i)}}} \right){\alpha_{l}^{2}(i)}}}}} & (28)\end{matrix}$

for l=1, . . . , L. Then, the outputs from finger l, l=1, . . . , L, arecombined for a Rake receiver to obtain the transmitted traffic datad_(trafic)(k_(bit)) at “Σ” 129 in FIG. 2. Walsh demodulation isperformed by multiplying with W₂ ⁴(i) and accumulating over at$\sum\limits_{4}$

205 in FIG. 2. The overall output 207 is written as

R _(data)(k _(bit))≈cd _(trafic)(k _(bit))  (29)

where c is a positive constant, k_(bit) is the traffic channel bitindex, and four chips per bit are used with W₂ ⁴(i) The soft decisionvariable R_(data)(k_(bit)) is used for a soft decision decoder. The harddecision value would be the sign of R_(data)(k_(bit)).

Again, the weight vector automatically compensates for phase distortion,and therefore no separate phase calibration is needed.

SIMULATION RESULTS

The simulation system parameters are listed in TABLES 1 and 2 for aW-CDMA and a CDMA2000 system, respectively, in accordance withembodiments of the invention.

TABLE 1 System simulation parameters used for a W-CDMA system such asshown in FIG. 1. DESCRIPTION NOTATION VALUE Data rate R_(b) 960 kbpsChip rate R_(c) 3.84 Mcps Carrier Frequency f₀ 1.95 GHz Pilot dataspreading gain SF_(DPDCH) 256 Pilot data Walsh symbol C_(ch,256.0) All1's Traffic data spreading gain SF_(DPCCH) 4 Traffic data Walsh symbolC_(ch,4.2) 1, −1, 1, −1 Convolutional code Not used Mobile speed ν 50km/h Multipath fading model Jakes Fading Number of multipaths L 2Convergence parameter for smart antenna μ 1.5 Positive constant forsmart antenna in α 0.1 equations (13) and (16) Initial DOA θ₀ 0° DOAincrement of the desired signal Δθ 3.7e-05° per snapshot Uniformlydistributed random phase φ_(I), . . ., φ_(M) Random distortions due tomixers (0, 2π)

TABLE 2 Simulation system parameters used for a CDMA2000 system, such asshown in FIG. 2. DESCRIPTION NOTATION VALUE Data rate R_(b) 76.8 kbpsChip Rate R_(c) 1.2288 Mcps Carrier frequency f₀ 1.95 GHz Pilot dataspreading gain SF_(pilot) 32 Pilot data Walsh symbol W₀ ³² All 1'sTraffic data spreading gain SF_(traffic) 4 Traffic data Walsh symbol W₂⁴ 1, 1, −1, −1 Convolutional Code Not used Mobile speed ν 50 km/hMultipath fading model Jakes Fading Number of multipaths L 2 Convergenceparameter for smart antenna μ 1.5 Positive constant for smart antenna inα 0.1 equations (13) and (16) Initial DOA θ₀ 0° DOA increment of thedesired signal Δθ 3.7e-05° per snapshot Uniformly distributed randomphase φ_(I), . . ., φ_(M) Random distortions due to the mixers (0, 2π)

The Jakes Fading of Tables 1 and 2 is discussed, for example, in W. C.Jr., Jakes, Microwave Mobile Communications, Wiley-Interscience, 1974,pp. 65-78.

FIG. 3 is a simulation showing a tracking capability at each element ofM=3 elements when a smart antenna with the conventional N-LMS algorithmis used for a W-CDMA system such as in FIG. 1. FIG. 3A, 3B, and 3Cillustrate the Average Phase Over Slot Interval in Radian, for 1^(st),2^(nd) and 3^(rd) antenna element, respectively.

FIG. 4 is a simulation showing the corresponding tracking capability ofthe MN-LMS smart antenna algorithm with the MN-LMS algorithm. FIG. 4A,4B and 4C illustrate the Average Phase over Slot Interval in Radian, for1^(st), 2^(nd) and 3^(rd) antenna element, respectively. FIG. 4 informsthat the phase of the each element in the weight vector converges to theindividual input total phase, which is the sum of the DOA, fading phase,and the phase distortion due to the mixers. The output phase by usingMN-LMS algorithm in the present invention is close to the total inputphase as shown in FIG. 4. The tracking capability of the conventionalN-LMS algorithm in FIG. 3 shows a little bit worse performance than thatof the MN-LMS in FIG. 4.

FIG. 5 shows simulation bit error rate (BER) results of the MN-LMSalgorithm with the number of antenna element M as a parameter, e.g., M=1and 3 for a W-CDMA reverse link. BER results for the N-LMS algorithm arealso shown for comparison. FIG. 5 also shows that the smart antenna ofthe MN-LMS algorithm in the present invention is 1 dB better inbit-energy-to-noise plus interference ratio E_(b)/(N₀o+I₀) than theconventional N-LMS algorithm at BER=10⁻³ when M=3. In addition, FIG. 5shows that significant BER improvement, e.g., about 5 dB improvement inE_(b)/(N₀+I₀), can be achieved by employing the smart antenna when M=3elements, compared to a single antenna.

FIG. 6 shows the corresponding simulation BER results for a CDMA2000reverse link. Similar observations are also observed in FIG. 6. Thesimulated BER results at E_(b)/(N₀₊I₀)=25 dB may be inadequate due toinsufficient simulation runs. It is anticipated that actual results willresult in a smooth curve.

In conclusion, the smart antenna with the MN-LMS algorithm in thepresent invention does not require any phase calibration for thedifferent RF mixers phase distortions. In addition, separate channelestimation is not used for demodulation in the present invention.Furthermore, the smart antenna with the MN-LMS in the present inventionyields better BER results than a smart antenna with a conventional N-LMSalgorithm. Finally, the smart antenna with the N-LMS or MN-LMS algorithmat MN-LMS smart antenna requires a linear order of M complexmultiplications, e.g., (5M+2) complex multiplication, and a linear orderof complex additions, e.g., (4M+1) complex additions per snapshot, whichcan be implemented with a modern chip technology. This is a significantdifference over conventional smart antenna technology which may requiremore than M² order of computations.

While the preferred mode and best mode for carrying out the inventionhave been described, those familiar with the art to which this inventionrelates will appreciate that various alternative designs and embodimentsfor practicing the invention are possible, and will fall within thescope of the following claims.

What is claimed is:
 1. A method of receiving a signal for use incombination with wireless communications, comprising the steps of: (A)receiving a signal in a plurality of antennas; and (B) processing thereceived signal utilizing an updated weight vector, wherein the updatedweight vector compensates substantially for a phase distortion of thesignal, wherein the received signal is processed according to:$\begin{matrix}{{{\underset{\_}{w}}_{l}\left( {i + 1} \right)} = \quad {{{\underset{\_}{w}}_{l}(i)} + {\frac{\mu}{a + {{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}}^{2}} \times \left\lbrack {{M{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}} - {{{\underset{\_}{\overset{\sim}{y}}}_{l}^{H}(i)}{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}{{\underset{\_}{w}}_{l}(i)}}} \right\rbrack}}} \\{= \quad {{{\underset{\_}{w}}_{l}(i)} + {\frac{\mu}{a + {{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}}^{2}} \times {\left\lbrack {{M{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}} - {{{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}}^{2}{{\underset{\_}{w}}_{l}(i)}}} \right\rbrack.}}}}\end{matrix}$


2. The method of claim 1, wherein the plurality of antennas is amultiple antenna array.
 3. The method of claim 1, wherein the pluralityof antennas is multiple antennas.
 4. The method of claim 1, the methodnot including a step of phase calibration.
 5. The method of claim 1,wherein the plurality of antennas are in a base station.
 6. The methodof claim 1, wherein the plurality of antennas are in a mobile station.7. A method of receiving a signal for use in combination with wirelesscommunications, comprising the steps of: (A) receiving a signal in aplurality of antennas; and (B) processing the received signal utilizingan updated weight vector, wherein the updated weight vector compensatessubstantially for a phase distortion of the signal, wherein the receivedsignal is processed according to${{\underset{\_}{w}}_{l}\left( {i + 1} \right)} = {{{\underset{\_}{w}}_{l}(i)} + {\frac{\mu}{a + {{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}}^{2}} \times {\left\lbrack {{M{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}} - {{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}{{\underset{\_}{\overset{\sim}{y}}}_{l}^{H}(i)}{{\underset{\_}{w}}_{l}(i)}}} \right\rbrack.}}}$


8. The method of claim 7, wherein the plurality of antennas is amultiple antenna array.
 9. The method of claim 7, wherein the pluralityof antennas is multiple antennas.
 10. The method of claim 7, the methodnot including a step of phase calibration.
 11. The method of claim 7,wherein the plurality of antennas are in a base station.
 12. The methodof claim 7, wherein the plurality of antennas are in a mobile station.13. A system for receiving a signal for use in combination with wirelesscommunications, comprising: (A) at least one signal processor,responsive to a signal received in a plurality of antennas, forprocessing the received signal utilizing an updated weight vector,wherein the updated weight vector compensates substantially for a phasedistortion of the signal; and (B) wherein the received signal isprocessed according to: $\begin{matrix}{{{\underset{\_}{w}}_{l}\left( {i + 1} \right)} = \quad {{{\underset{\_}{w}}_{l}(i)} + {\frac{\mu}{a + {{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}}^{2}} \times \left\lbrack {{M{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}} - {{{\underset{\_}{\overset{\sim}{y}}}_{l}^{H}(i)}{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}{{\underset{\_}{w}}_{l}(i)}}} \right\rbrack}}} \\{= \quad {{{\underset{\_}{w}}_{l}(i)} + {\frac{\mu}{a + {{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}}^{2}} \times {\left\lbrack {{M{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}} - {{{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}}^{2}{{\underset{\_}{w}}_{l}(i)}}} \right\rbrack.}}}}\end{matrix}$


14. The system of claim 13, wherein the plurality of antennas ismultiple antennas.
 15. The system of claim 13, the method not includinga step of phase calibration.
 16. The system of claim 13, furthercomprising a base station, wherein the plurality of antennas are in thebase station.
 17. The system of claim 13, further comprising a mobilestation, wherein the plurality of antennas are in the mobile station.18. A system for receiving a signal for use in combination with wirelesscommunications, comprising: (A) at least one signal processor,responsive to a signal received in a plurality of antennas, forprocessing the received signal utilizing an updated weight vector,wherein the updated weight vector compensates substantially for a phasedistortion of the signal; and (B) wherein the received signal isprocessed according to:${{\underset{\_}{w}}_{l}\left( {i + 1} \right)} = {{{\underset{\_}{w}}_{l}(i)} + {\frac{\mu}{a + {{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}}^{2}} \times {\left\lbrack {{M{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}} - {{{\underset{\_}{\overset{\sim}{y}}}_{l}(i)}{{\underset{\_}{\overset{\sim}{y}}}_{l}^{H}(i)}{{\underset{\_}{w}}_{l}(i)}}} \right\rbrack.}}}$


19. The system of claim 18, wherein the plurality of antennas ismultiple antennas.
 20. The system of claim 18, the method not includinga step of phase calibration.
 21. The system of claim 18, furthercomprising a base station, wherein the plurality of antennas are in thebase station.
 22. The system of claim 18, further comprising a mobilestation, wherein the plurality of antennas are in the mobile station.